Question

simplify the expression (9+4i)^2

Answer 1

(9+4i)^2

(9+4i) (9+4i)

FOIL

first = 9*9 =81

outer = 9*4i = 36i

inner = 4i*9 = 36i

last = 4i*4i = 16 i^2    (i^2 = -1) so 16 *(-1) = -16

add them together

81+ 36i + 36i-16

81-16+36i+36i

65+72i

Answer 2

Answer:

65+72i

Step-by-step explanation:

The given expression is

$(9+4i)^2$

We need to find the simplified form of given expression.

Using perfect square formula, we get

$(9+4i)^2=(9)^2+2(9)(4i)+(4i)^2$       $[\because (a+b)^2=a^2+2ab+b^2]$

$(9+4i)^2=81+72i+(4)^2(i)^2$

$(9+4i)^2=81+72i+16(-1)$                     $[\because i^2=-1]$

On further simplification we get

$(9+4i)^2=81+72i-16$  

Combined like terms.

$(9+4i)^2=(81-16)+72i$  

$(9+4i)^2=65+72i$

Therefore, the simplified form of given expression is 65+72i.